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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Sebastian Raschka*  \n",
      "last modified: 03/31/2014"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem Category\n",
      "- Statistical Pattern Recognition   \n",
      "- Supervised Learning  \n",
      "- Parametric Learning  \n",
      "- Bayes Decision Theory  \n",
      "- Multivariate data (2-dimensional)\n",
      "- 2-class problem\n",
      "- different variances\n",
      "- equal prior probabilities\n",
      "- Gaussian model (2 parameters)\n",
      "- with conditional Risk (1-0 loss functions)\n",
      "<hr>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p><a name=\"sections\"></a>\n",
      "<br></p>\n",
      "\n",
      "# Sections\n",
      "\n",
      "\n",
      "<p>&#8226; <a href=\"#given\">Given information</a><br>\n",
      "&#8226; <a href=\"#deriving_db\">Deriving the decision boundary</a><br>\n",
      "&#8226; <a href=\"#classify_rand\">Classifying some random example data</a><br>\n",
      "&#8226; <a href=\"#emp_err\">Calculating the empirical error rate</a><br>\n",
      "\n",
      "  \n",
      "\n",
      "  \n",
      "  \n",
      "\n",
      "\n",
      "\n",
      "<hr>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p><a name=\"given\"></a>\n",
      "<br></p>\n",
      "\n",
      "## Given information:\n",
      "\n",
      "[<a href=\"#sections\">back to top</a>] <br>\n",
      "\n",
      "<br> \n",
      "####model: continuous univariate normal (Gaussian) model for the class-conditional densities\n",
      "\n",
      "\n",
      "$ p(\\vec{x} | \\omega_j) \\sim N(\\vec{\\mu}|\\Sigma) $ \n",
      "\n",
      "$ p(\\vec{x} | \\omega_j) \\sim \\frac{1}{(2\\pi)^{d/2} |\\Sigma|^{1/2}} \\exp{ \\bigg[-\\frac{1}{2} (\\vec{x}-\\vec{\\mu})^t \\Sigma^{-1}(\\vec{x}-\\vec{\\mu}) \\bigg] } $\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "####Prior probabilities:\n",
      "\n",
      "$ P(\\omega_1) = P(\\omega_2) = 0.5 $\n",
      "\n",
      "<br>\n",
      "\n",
      "####Loss functions:\n",
      "\n",
      "where \n",
      "\n",
      "$ \\lambda(\\alpha_i|\\omega_j) = \\lambda_{ij}$,  \n",
      "\n",
      "the loss occured if $action_i$ is taken if the actual true class is $ \\omega_j$ (assuming that $action_i$ classifies sample as $\\omega_i$)\n",
      "\n",
      "\\begin{equation}\n",
      "\\lambda = \\begin{pmatrix}\n",
      "\\lambda_{11} \\quad \\lambda_{12} \\\\\n",
      "\\lambda_{21} \\quad \\lambda_{22}\n",
      "\\end{pmatrix}\n",
      "= \\begin{pmatrix}\n",
      "0 \\quad 1 \\\\\n",
      "1 \\quad 0 \\\\\n",
      "\\end{pmatrix}\\\\\n",
      "\\end{equation}\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The samples are of 2-dimensional feature vectors:\n",
      "\n",
      "$ \\vec{x} = \\bigg[ \n",
      "\\begin{array}{c}\n",
      "x_1 \\\\\n",
      "x_2 \\\\\n",
      "\\end{array} \\bigg] $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Means of the sample distributions for 2-dimensional features:\n",
      "\n",
      "$ \\vec{\\mu}_{\\,1} = \\bigg[ \n",
      "\\begin{array}{c}\n",
      "0 \\\\\n",
      "0 \\\\\n",
      "\\end{array} \\bigg] $,\n",
      "$ \\; \\vec{\\mu}_{\\,2} = \\bigg[ \n",
      "\\begin{array}{c}\n",
      "1 \\\\\n",
      "2 \\\\\n",
      "\\end{array} \\bigg] $\n",
      "\n",
      "#### Covariance matrices for the statistically independend and identically distributed ('i.i.d') features: \n",
      "\n",
      "$ \\Sigma_i = \\bigg[ \n",
      "\\begin{array}{cc}\n",
      "\\sigma_{11}^2 & \\sigma_{12}^2\\\\\n",
      "\\sigma_{21}^2 & \\sigma_{22}^2 \\\\\n",
      "\\end{array} \\bigg], \\; \n",
      "\\Sigma_1 = \\bigg[ \n",
      "\\begin{array}{cc}\n",
      "1 & 0\\\\\n",
      "0 & 1 \\\\\n",
      "\\end{array} \\bigg], \\;  \n",
      "\\Sigma_1 = \\bigg[ \n",
      "\\begin{array}{cc}\n",
      "2 & 0\\\\\n",
      "0 & 2 \\\\\n",
      "\\end{array} \\bigg] $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p><a name=\"deriving_db\"></a>\n",
      "<br></p>\n",
      "\n",
      "## Deriving the decision boundary\n",
      "[<a href=\"#sections\">back to top</a>] <br>\n",
      "\n",
      "### Bayes' Rule:\n",
      "\n",
      "\n",
      "$ P(\\omega_j|x) = \\frac{p(x|\\omega_j) * P(\\omega_j)}{p(x)}$ \n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Risk Functions:\n",
      "\n",
      "$ R(\\alpha_1|\\;\\vec{x}) = \\lambda_{11}P(\\omega_1|\\;\\vec{x}) + \\lambda_{12}P(\\omega_2|\\;\\vec{x}) $\n",
      "\n",
      "$ R(\\alpha_2|\\;\\vec{x}) = \\lambda_{21}P(\\omega_1|\\;\\vec{x}) + \\lambda_{22}P(\\omega_2|\\;\\vec{x}) $\n",
      "\n",
      "<br>\n",
      "with 1-0 loss function:\n",
      "\n",
      "$ R(\\alpha_1|\\; \\vec{x}) = P(\\omega_2|\\;\\vec{x}) = 1 -  P(\\omega_1|\\;\\vec{x})  $\n",
      "\n",
      "$ R(\\alpha_2|\\;\\vec{x}) = P(\\omega_1|\\;\\vec{x}) = 1 -  P(\\omega_2|\\;\\vec{x}) $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Discriminant Functions:\n",
      "\n",
      "The goal is to maximize the discriminant function, which we define as the posterior probability here to perform a **minimum-error classification** (Bayes classifier).\n",
      "\n",
      "$ g_1(\\vec{x}) = P(\\omega_1 | \\; \\vec{x}), \\quad  g_2(\\vec{x}) = P(\\omega_2 | \\; \\vec{x})$\n",
      "\n",
      "$ \\Rightarrow g_1(\\vec{x}) = P(\\vec{x}|\\;\\omega_1) \\;\\cdot\\; P(\\omega_1) \\quad | \\; ln \\\\\n",
      "\\quad g_2(\\vec{x}) = P(\\vec{x}|\\;\\omega_2) \\;\\cdot\\; P(\\omega_2) \\quad | \\; ln $\n",
      "\n",
      "<br>\n",
      "We can drop the prior probabilities (since we have eual priors in this case): \n",
      "\n",
      "$ \\Rightarrow g_1(\\vec{x}) = ln(P(\\vec{x}|\\;\\omega_1))  \\\\\n",
      "\\quad g_2(\\vec{x}) = ln(P(\\vec{x}|\\;\\omega_2))  $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\Rightarrow g_1(\\vec{x}) = \\vec{x}^{\\,t} - \\frac{1}{2} \\Sigma_1^{-1} \\vec{x} + \\bigg( \\Sigma_1^{-1} \\vec{\\mu}_{\\,1}\\bigg)^t + \\bigg( -\\frac{1}{2} \\vec{\\mu}_{\\,1}^{\\,t} \\Sigma_{1}^{-1} \\vec{\\mu}_{\\,1} -\\frac{1}{2} ln(|\\Sigma_1|)\\bigg)   \\\\\n",
      "\\quad g_2(\\vec{x}) = \\vec{x}^{\\,t} - \\frac{1}{2} \\Sigma_2^{-1} \\vec{x} + \\bigg( \\Sigma_2^{-1} \\vec{\\mu}_{\\,2}\\bigg)^t + \\bigg( -\\frac{1}{2} \\vec{\\mu}_{\\,2}^{\\,t} \\Sigma_{2}^{-1} \\vec{\\mu}_{\\,2} -\\frac{1}{2} ln(|\\Sigma_2|)\\bigg)  $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr>\n",
      "**Let:**\n",
      "\n",
      "$\\vec{W}_{\\,i} = - \\frac{1}{2} \\Sigma_i^{-1}\\\\\n",
      "\\vec{w}{\\,i} =  \\bigg( \\Sigma_i^{-1} \\vec{\\mu}_{\\,i} \\bigg)^t\\\\\n",
      "\\omega_{i0} = \\bigg( -\\frac{1}{2} \\vec{\\mu}_{\\,i}^{\\,t} \\Sigma_{i}^{-1} \\vec{\\mu}_{\\,i} -\\frac{1}{2} ln(|\\Sigma_i|)\\bigg)$\n",
      "<hr>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\vec{W}_{\\,1} = \\bigg[ \n",
      "\\begin{array}{cc}\n",
      "(1/4) & 0\\\\\n",
      "0 & (1/4) \\\\\n",
      "\\end{array} \\bigg] $\n",
      "\n",
      "$ \\vec{w}_{\\,1} = \\bigg[ \n",
      "\\begin{array}{cc}\n",
      "(1/4) & 0\\\\\n",
      "0 & (1/4) \\\\\n",
      "\\end{array} \\bigg] \\cdot \\bigg[ \n",
      "\\begin{array}{c}\n",
      "0 \\\\\n",
      "0 \\\\\n",
      "\\end{array} \\bigg] = \\bigg[ \n",
      "\\begin{array}{c}\n",
      "0 \\\\\n",
      "0 \\\\\n",
      "\\end{array} \\bigg]$ "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\omega_{10} = -\\frac{1}{2} [0 \\quad 0 ] \\bigg[ \n",
      "\\begin{array}{cc}\n",
      "(1/4) & 0\\\\\n",
      "0 & (1/4) \\\\\n",
      "\\end{array} \\bigg] \\cdot \\bigg[ \n",
      "\\begin{array}{c}\n",
      "0 \\\\\n",
      "0 \\\\\n",
      "\\end{array} \\bigg] \n",
      "- ln(2) = -ln(2)$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\vec{W}_{\\,2} = \\bigg[ \n",
      "\\begin{array}{cc}\n",
      "(-1/2) & 0\\\\\n",
      "0 & (-1/2) \\\\\n",
      "\\end{array} \\bigg] $\n",
      "\n",
      "$ \\vec{w}_{\\,2} = \\bigg[ \n",
      "\\begin{array}{c}\n",
      "1 \\\\\n",
      "2 \\\\\n",
      "\\end{array} \\bigg]$ "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\omega_{20} = -\\frac{1}{2} [1 \\quad 2 ] \\bigg[ \n",
      "\\begin{array}{cc}\n",
      "(1/4) & 0\\\\\n",
      "0 & (1/4) \\\\\n",
      "\\end{array} \\bigg] \\cdot \\bigg[ \n",
      "\\begin{array}{c}\n",
      "1 \\\\\n",
      "2 \\\\\n",
      "\\end{array} \\bigg] \n",
      "- \\frac{1}{2}ln(1) = -2.5$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\Rightarrow g_1(\\vec{x}) = \\vec{x}^{\\,t} \\bigg[ \n",
      "\\begin{array}{cc}\n",
      "(1/4) & 0\\\\\n",
      "0 & (1/4) \\\\\n",
      "\\end{array} \\bigg] \n",
      "\\vec{x} + \\bigg[\n",
      "\\begin{array}{c}\n",
      "0 \\\\\n",
      "0 \\\\\n",
      "\\end{array} \\bigg]^t - ln(2) = \\vec{x}^{\\,t} - \\frac{1}{4} \\vec{x} - ln(2)$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\Rightarrow g_2(\\vec{x}) = \\vec{x}^{\\,t} \\bigg[ \n",
      "\\begin{array}{cc}\n",
      "(-1/2) & 0\\\\\n",
      "0 & (-1/2) \\\\\n",
      "\\end{array} \\bigg] \n",
      "\\vec{x} + \\bigg[\n",
      "\\begin{array}{c}\n",
      "1 \\\\\n",
      "2 \\\\\n",
      "\\end{array} \\bigg]^t \\vec{x} -2.5 = \\vec{x}^{\\,t} - \\frac{1}{2} \\vec{x} + [1 \\quad 2] \\; \\vec{x} - 2.5$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Decision Boundary\n",
      "\n",
      "$g_1(\\vec{x}) = g_2(\\vec{x}) $ \n",
      "\n",
      "$ \\Rightarrow \\vec{x}^{\\,t} - \\frac{1}{4} \\vec{x} - ln(2) = \\vec{x}^{\\,t} - \\frac{1}{2} \\vec{x} + [1 \\quad 2] \\; \\vec{x} - 2.5 \\quad \\bigg| \\; \\cdot \\; 4$\n",
      "\n",
      "$ \\Rightarrow \\vec{x}^{\\,t} -  \\vec{x} - 4ln(2) = \\vec{x}^{\\,t} - 2 \\vec{x}+ 4 \\;( [1 \\quad 2] \\; \\vec{x}) - 10 $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\Rightarrow [x_1 \\quad x_2] \\cdot \\bigg(-\\bigg[ \\begin{array}{c}\n",
      "x_1 \\\\\n",
      "x_2 \\\\\n",
      "\\end{array}\\bigg] \\bigg) -4ln(2) = [x_1 \\quad x_2] \\cdot \\bigg(-\\bigg[ \\begin{array}{c}\n",
      "2x_1 \\\\\n",
      "2x_2 \\\\\n",
      "\\end{array}\\bigg] \\bigg) + [4 \\quad 8] \\cdot \n",
      "\\bigg[ \\begin{array}{c}\n",
      "x_1 \\\\\n",
      "x_2 \\\\\n",
      "\\end{array}\\bigg] -10$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\Rightarrow -x_1^2 - x_2^2 - 4ln(2) = -2x_1^2 - 2x_2^2 + 4x_1 + 8x_2 -10 $\n",
      "\n",
      "$ \\Rightarrow x_1^2 + x_2^2 -4x_1 - 8x_2 - 4ln(2) + 10 = 0 $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p><a name=\"classify_rand\"></a>\n",
      "<br></p>\n",
      "\n",
      "## Classifying some random example data\n",
      "\n",
      "[<a href=\"#sections\">back to top</a>] <br>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "\n",
      "import numpy as np\n",
      "from matplotlib import pyplot as plt\n",
      "\n",
      "def decision_boundary(x_1):\n",
      "    \"\"\" Calculates the x_2 value for plotting the decision boundary.\"\"\"\n",
      "    return 4 - np.sqrt(-x_1**2 + 4*x_1 + 6 + np.log(16))\n",
      "\n",
      "def decision_rule(x_vec)\n",
      "x_1^2 + x_2^2 - -4x_1 - 8x_2 - 4ln(2) + 10 = 0\n",
      "\n",
      "\n",
      "# Generate 100 random patterns for class1\n",
      "mu_vec1 = np.array([0,0])\n",
      "cov_mat1 = np.array([[2,0],[0,2]])\n",
      "x1_samples = np.random.multivariate_normal(mu_vec1, cov_mat1, 100)\n",
      "mu_vec1 = mu_vec1.reshape(1,2).T # to 1-col vector\n",
      "\n",
      "# Generate 100 random patterns for class2\n",
      "mu_vec2 = np.array([1,2])\n",
      "cov_mat2 = np.array([[1,0],[0,1]])\n",
      "x2_samples = np.random.multivariate_normal(mu_vec2, cov_mat2, 100)\n",
      "mu_vec2 = mu_vec2.reshape(1,2).T # to 1-col vector\n",
      "\n",
      "# Scatter plot\n",
      "f, ax = plt.subplots(figsize=(7, 7))\n",
      "ax.scatter(x1_samples[:,0], x1_samples[:,1], marker='o', color='green', s=40, alpha=0.5)\n",
      "ax.scatter(x2_samples[:,0], x2_samples[:,1], marker='^', color='blue', s=40, alpha=0.5)\n",
      "plt.legend(['Class1 (w1)', 'Class2 (w2)'], loc='upper right') \n",
      "plt.title('Densities of 2 classes with 100 bivariate random patterns each')\n",
      "plt.ylabel('x2')\n",
      "plt.xlabel('x1')\n",
      "ftext = 'p(x|w1) ~ N(mu1=(0,0)^t, cov1=2*I)\\np(x|w2) ~ N(mu2=(1,2)^t, cov2=I)'\n",
      "plt.figtext(.15,.8, ftext, fontsize=11, ha='left')\n",
      "\n",
      "# Plot decision boundary\n",
      "x_1 = np.arange(-5, 5, 0.1)\n",
      "bound = decision_boundary(x_1)\n",
      "plt.plot(x_1, bound, 'r--', lw=4)\n",
      "\n",
      "x_vec = np.linspace(*ax.get_xlim())\n",
      "x_1 = np.arange(0, 100, 0.05)\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "-c:8: RuntimeWarning: invalid value encountered in sqrt\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SCtKQVpCGgooCzO09F6b6prAR2UBGMshI0eJ6Uv4EruauKssiFovx5ZdfYu7c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\nF19c8HFPPPFE4M+LFy/G4sWLQ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       "text": [
        "<matplotlib.figure.Figure at 0x106215210>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p><a name=\"emp_err\"></a>\n",
      "<br></p>\n",
      "\n",
      "## Calculating the empirical error rate\n",
      "\n",
      "[<a href=\"#sections\">back to top</a>] <br>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def decision_rule(x_vec):\n",
      "    \"\"\" Returns value for the decision rule of 2-d row vectors \"\"\"\n",
      "    x_1 = x_vec[0]\n",
      "    x_2 = x_vec[1]\n",
      "    return x_1**2 + x_2**2 -4*x_1 - 8*x_2 - 4*np.log(2) + 10\n",
      "\n",
      "w1_as_w2, w2_as_w1 = 0, 0\n",
      "\n",
      "for x in x1_samples:\n",
      "    if decision_rule(x) < 0:\n",
      "        w1_as_w2 += 1\n",
      "for x in x2_samples:\n",
      "    if decision_rule(x) > 0:\n",
      "        w2_as_w1 += 1\n",
      "\n",
      "emp_err = (w1_as_w2 + w2_as_w1) / float(len(x1_samples) + len(x2_samples))\n",
      "    \n",
      "print('Empirical Error: {}%'.format(emp_err * 100))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Empirical Error: 19.5%\n"
       ]
      }
     ],
     "prompt_number": 17
    }
   ],
   "metadata": {}
  }
 ]
}